P[11]'s response to Q5. "We see at first the triangles ΓΘA and ΘΔA. We know that Θ is the perpendicular bisector of Γ and Δ [sic]. Thus, ΓΘ = ΘΔ. We have also common side ΘA thus also ΓA and AΔ are equal sides. Thus, for the triangles ABΓ and ABΔ we have AB common side, ΓA and AΔ equal sides and the angle B equal because it is divided by AB, thus they are equidistant B 1 and B 2 . From all the above the triangles ABΓ and ABΔ are equal."

Context in source publication

Context 1

... proof can start from noticing that line (ζ) is an axis of symmetry (even though, as the teacher noted to us, students are accustomed to seeing axes of symmetry drawn vertically, not horizontally). P [11] (Figure 2) makes a remarkable attempt to establish the validity of the three claims that will allow drawing the conclusion that triangles ABΓ and ΑΒΔ are congruent through, most probably, a version of the SAS criterion. The student first establishes two of these three claims: AB = AB, a common side; and, ΓΘ = ΘΔ, because line (ζ) is a perpendicular bisector of line (ε). ...